I have a pupil working on her Grade 3 piano and in all my 35 years of playing, I have never come across SOPRA (meaning ABOVE/ON). In the Allegretto by Turk there are three. It is a study for crossing hands, therefore, could anyone confirm that it should be played firstly as the left hand over right to play a top F# and then followed by a middle D (LH over RH)and then lastly, a top G again LH over RH.

Am I being thick or have I got this right? :

I agree with your interpretation of bar 9, but bar 12 looks like RH over LH playing D two octaves below middle C; bar 17 is LH over RH starting on G above middle C, not high G. In the last example it's only with middle D that there's actually any crossing.

That way it has three different versions of hand-crossing: the whole arm crossing both directions and one hand playing directly underneath the other (bar 17).

I have had two students who played this piece in their exams - I really like it and so did they.

Thank you, I think I've got it! Am I right in thinking that the word SOPRA is for the hands going on top and above and doesn't apply at all to the notes. I think that's why I was confused.

Yes, Sopra refers to what the hand does and not the notes.
If the notes were at a different octave the 8va sign would be used.